Karlsson, playing with fellow Swede Henrik Stenson, produced a half a dozen birdies on the back nine to close the gap on Phil Mickelson and Hunter Mahan, going on to halve the match at the end of the day’s play.
“We withstood that to get a half,” said an exhausted but happy Mickelson.
Both Karlsson and Mahan had eagle putts at 18, but both failed to sink them as they settled for a share of the spoils.
The Swedish pair had won the first hole, but Mickelson and Mahan won the next two to go one up.
Mickelson eagled the par five seventh to put the Americans two up, while at the ninth Mahan holed an impressive birdie putt only for Karlsson to respond with a long putt of his own to keep the Americans from extending the lead.
The Europeans won 12 and 13 and squared the match thanks to back-to-back
birdies from Karlsson.
The Americans will go into the final day of the trans-Atlantic match play show case with the lead for the first time since 1995, after splitting the fourball matches 2-2 – with one win for each team and two matches halved in a performance that promised final day fireworks.
The Americans had seen their first-day momentum wane as as Europe earned 2.5 points in Saturday morning’s foursomes to the 1.5 of the hosts.
That cut their overnight deficit by a point, and that’s where matters still stood after the fourballs, three of which came down to the 18th hole.
“It has really been amazing,” Azinger said of the evening’s close. “My stomach is just churning.”
Earlier, Mickelson and Anthony Kim succumbed 2 and 1 to Stenson and Ryder Cup debutant Oliver Wilson in the foursomes.
Mickelson and Kim had been four up through six in that match but didn’t win another hole.
Wilson made his first Ryder Cup match one to remember, holing a snaking 7 metre putt for a birdie at 17 that sealed the win.
“We still fought hard,” Mickelson said of the foursomes. “It looked like we were going to bring that thing down to the end until that long putt on 17 by Oliver Wilson that sealed it.
“But we fought hard all day, and Hunter and I hung in there, and obviously we wanted to win, we had opportunities for that. But as well as Karlsson played, as many birdies as he made, a half point isn’t bad.”
Steve Stricker and Ben Curtis halved a classic battle with Sergio Garcia and Paul Casey, Stricker holing a clutch 15-foot putt at 18, where he had been in the greenside rough.
Casey, who had struggled on the greens all afternoon, stepped up and made his own 2.5 metre putt to hang onto the half point.
The Americans had held a slim lead over most of the front nine, going one up at the second and staying there through the turn before Garcia birdied 10 to square the match.
Stricker had a chance to preserve the lead there but missed his birdie putt, and it stayed all square the rest of the way.
Ian Poulter continued his superb Ryder Cup performance, teaming with Graeme McDowell to beat Americans Kenny Perry and Jim Furyk one up on Saturday.
Poulter holed the metre putt to halve 18 and preserve the victory, but McDowell made his share of crucial putts as they kept the Americans at bay on the back nine.
Poulter’s birdie at the first hole gave him and McDowell a one up lead over Perry and Furyk, but the Americans won the next hole to get to all square. It stayed that way until the seventh, where Poulter drained another winning putt for a one up lead.
At the ninth, Poulter landed his approach two metres from the pin and made that. Perry spun his ball past the hole to about 1.3 metres, but pushed his putt right to give Europe a two up advantage.
Perry’s birdie at 14 cut the lead to one up with four to play.
Poulter had already teamed with Justin Rose for a 4 and 3 foursomes victory over Stewart Cink and Chad Campbell.
McDowell had nailed a two metre putt at the last to win the hole and halve his and Miguel Angel Jimenez’s foursomes against Justin Leonard and Hunter Mahan.
“He has been absolutely amazing,” Faldo said of McDowell. “That was why it was a great swap to put him with Poulter this afternoon, because you’ve got two guys just absolutely bouncing.”
It was a disappointing turnaround for Furyk and Perry, however, who had won their foursomes against Padraig Harrington and Karlsson 3 and 1.
The crowd-pleasing pairing of Boo Weekley and Kentuckian JB Holmes boosted US morale with a 2 and 1 victory over Lee Westwood and Soren Hansen in the first fourball.
The US pair moved three up at 10, courtesy of a Holmes eagle, but Westwood and Hansen managed to pull back to one down through 13.
The Americans regained a two up lead at the next and held onto it to the delight of the “Boo-S-A” chanting crowd.
Their victory put an end to Westwood’s 12-match unbeaten streak in the Ryder Cup – the all-time record he shares with US legend Arnold Palmer.
The final day of the Ryder Cup on Sunday will see all the players involved in the singles with US captain Paul Azinger opting to put all his form players out on the course in the early games.
Spain’s Sergio Garcia will meet Anthony Kim in the first match while Europe captain Nick Faldo has opted to save his in-form players Ian Poulter and Graeme McDowell for match 10 and 9 respectively.
Swedes Robert Karlsson and Henrik Stenson will meet Justin Leonard and Kenny Perry in match 3 and 5 respectively.